Draftosaurus

From the publisher:

Your goal in Draftosaurus is to have the dino park most likely to attract visitors. To do so, you have to draft dino meeples and place them in pens that have some placement restrictions. Each turn, one of the players roll a die and this adds a constraint to which pens any other player can add their dinosaur. 

Draftosaurus is a quick and light drafting game in which you don't have a hand of cards that you pass around (after selecting one), but a bunch of dino meeples in the palm of your hand.